Course textbooks
For Math 8301/8302, there are two assigned course textbooks:
- Algebraic topology, by Allen Hatcher (freely available online).
- Introduction to topological manifolds, by John M. Lee.
These two textbooks cover the majority of the material that will be discussed in class. Hatcher's text gives an introduction to the fundamental group, homology, and cohomology, and will receive more emphasis in the first semester; Lee's textbook gives an introduction to the theory of point-set topology and topological manifolds.
However, there will be a nontrivial amount of material covered that does not come from these texts. Moreover, it is often beneficial to get several perspectives on the same material.
The following additional textbooks are placed on reserve in the math library:
- Algebraic topology: an introduction, by William S. Massey. This was published in 1967 and was, once, a standard textbook for an introductory course in algebraic topology. Most of our study of compact surfaces, covering spaces, and the fundamental group will be drawn from here.
- Algebraic topology: a first course, by Greenberg and Harper. This offers an alternative perspective on the material for the first semester.
- Topology from the differentiable viewpoint, by John Milnor. This is a relatively concise (and highly influential) set of notes on differential topology.
- Lectures on algebraic topology, by Albrecht Dold. This is a slightly more difficult, but also very careful, text covering much of what is in Hatcher's textbook, but also includes some very good material on manifolds.